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FINAL TOTAL RESOLUTION [RES300] · 5-CARD PROOF

Player 5 + 9 (9) vs. Banker 4 (Stands at 4): 5-Card Resolution #300

In walkthrough RES300, Player opens with A+4 (5) and draws fifth-card 9 (9) for a modulo-10 total of 4, while Banker opens with A+3 (4) and stands pat at 4 (5-card T outcome).

RES300 Player Path
P:5->4
RES300 Banker Path
B:4->4
RES300 Deal Length
5 Cards
RES300 Showdown
T (4v4)
Engine-Verified Scoreboard · 20 Hands

Read the Board at Table Speed

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Big Road P P B B P B B B P P P P B P P B B P P B
Big Eye Boy = = ≠ ≠ = ≠ = = ≠ ≠ ≠ ≠ ≠ = = = =
Small Road ≠ = ≠ ≠ ≠ = = ≠ ≠ = ≠ ≠ ≠ = =
Cockroach Pig = ≠ ≠ = ≠ = ≠ = = ≠ = ≠ ≠ ≠

Scoreboard sequence paired with 5-card resolution RES300 (P5+9->4 vs B4->4).

Big Road B is Banker, P is Player Roads under it Red (=): repeating Blue (≠): breaking
Step-by-Step Mark Proofs (Rule 1 & Rule 2)
Big Eye Boy Mark #3

Column 3 has 1 bead. Column 2 has 2 beads. Different depth → blue (≠).

  1. Column 4 starts, so use Rule 1: compare Column 3 with Column 2, 1 column further back.
  2. Column 3 has 1 bead. Column 2 has 2 beads. Different depth → blue (≠).

Common table reading watchout: Comparing the wrong columns. Compare Column 3, the one that just finished, with Column 2.

Small Road Mark #3

This bead is at Row 3. Column 2 stopped at Row 2, one row above → blue (≠).

  1. Column 4 goes down to Row 3, so use Rule 2: look 2 columns back, at Column 2.
  2. Column 2 stopped at Row 2, one row above → blue (≠).

Common table reading watchout: Thinking "no bead at this row" means blue. It is blue only when Column 2 stopped exactly one row above this bead.

Cockroach Pig Mark #3

Column 4 has 3 beads. Column 1 has 2 beads. Different depth → blue (≠).

  1. Column 5 starts, so use Rule 1: compare Column 4 with Column 1, 3 columns further back.
  2. Column 4 has 3 beads. Column 1 has 2 beads. Different depth → blue (≠).

Common table reading watchout: Comparing the wrong columns. Compare Column 4, the one that just finished, with Column 1.

Verified Reference Data

Key Facts & Table Specifications

RES300 Four-Card Opening Deal
Player A+4=5 vs Banker A+3=4

Verified non-natural start via handTotal([A,4])=5 and handTotal([A,3])=4.

RES300 Fifth-Card Modulo Proof
(5 + 9) mod 10 = 4 via 9

Player draws fifth-card 9 (value 9), transforming two-card 5 into three-card 4.

RES300 Banker Tableau Lookup
BANKER_TABLEAU[4][9] = false

Banker 4 stands pat at 4 without pulling sixth-card 5 (5).

RES300 Card Count & Winner
5 Cards -> T (4 vs 4)

Computed directly from resolveHand() with zero discretionary dealer options.

RES300 Derived Road Independence
Red (=) / Blue (≠) Symmetry Only

Big Eye Boy, Small Road, and Cockroach Pig compare Big Road column depths, not T vs B.

MODULO-10 ARITHMETIC · RES300

Step-by-Step Card Arithmetic for RES300: P(A+4)+9 vs B(A+3)

Canonical test [RES300] examines Player 5 (A+4) against Banker 4 (A+3); the fifth card 9 (9) brings Player's raw count to 14, which computes the single-digit remainder to 4.

[RES300-B] Under 4-point six-value gate (2..7) for [RES300], 9 (9) closes action at 5c with Banker at 4 (had 5=5 landed, 4+5=9 -> 9).

Complete 5-Card Resolution Trace for RES300
RES300 StageRES300 CardsRES300 Modulo MathRES300 Status
[RES300:Init]P(A+4)=5 vs B(A+3)=4playerShouldDraw(5)=true4-Card Deal
[RES300:5th]Player +9 (9)(5+9) mod 10 = 45th Card Sideways
[RES300:6th]Banker Stands (skip 5=5)Locked at 45-Card Final
[RES300:Settle]P=4 vs B=4Winner: TBig Road +T
  • [RES300-1] Confirm [RES300] opening P=5 (A+4) and B=4 (A+3) lack Natural 8/9.
  • [RES300-2] Add [RES300] fifth-card 9 (9) to P=5 for (5+9) mod 10 = 4.
  • [RES300-3] Run [RES300] BANKER_TABLEAU[4][9]=false to settle 4 vs 4 (T).
SETTLEMENT & SCOREBOARD · RES300

Showdown Settlement & Scoreboard Logging for RES300 (4 vs 4)

[RES300-C0] Comparing [RES300] final totals (5c), Player 4 vs Banker 4 awards [RES300] to Tie (T), which pushes main [RES300] Player/Banker wagers while settling [RES300] Tie bets at 8:1 or 9:1 and appends T to PPBBPBBBPP.

[RES300-D4] Side-bet & road check for [RES300] (P5+9->4 vs B4->4, 5c): [RES300] leaves [RES300] Dragon 7 inactive (needs winning 6c Banker 7, got 5c B=4) and leaves [RES300] Panda 8 inactive (needs winning 3c Player 8, got P=4); on [RES300] derived roads, Red (=) marks repeating Big Road depth and Blue (≠) marks breaking depth.

Table Reality Check

Myth vs. Truth

MythIn RES300, Banker 4 evaluates Player's three-card total (4) before deciding whether to draw.
TruthBanker 4 inspects only Player's fifth card 9 (value 9) via BANKER_TABLEAU[4][9] = false.
MythBecause RES300 resolves as T, the next derived-road mark must match T's colour.
TruthDerived roads record Red (=) when Big Road structure repeats and Blue (≠) when it breaks—never Banker or Player.
6 modules · 36 lessons · $25/month · Module 1 (10 lessons) free

Read Every Derived Road at Table Speed

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  • Structured step-by-step track across Foundations, Big Eye Boy, Small Road, and Cockroach Pig
  • 74 interactive lesson scoreboards and 94 inline quiz checks with plain-English mark feedback
  • Cloud Shoe Log and cross-device progress on web, iOS, and Android